Are Good-for-Games Automata Good for Probabilistic Model Checking?

  • Joachim Klein
  • David Müller
  • Christel Baier
  • Sascha Klüppelholz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8370)

Abstract

The potential double exponential blow-up for the generation of deterministic ω-automata for linear temporal logic formulas motivates research on weaker forms of determinism. One of these notions is the good-for-games property that has been introduced by Henzinger and Piterman together with an algorithm for generating good-for-games automata from nondeterministic Büchi automata. The contribution of our paper is twofold. First, we report on an implementation of this algorithms and exhaustive experiments. Second, we show how good-for-games automata can be used for the quantitative analysis of systems modeled by Markov decision processes against ω-regular specifications and evaluate this new method by a series of experiments.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Babiak, T., Blahoudek, F., Křetínský, M., Strejček, J.: Effective translation of LTL to deterministic rabin automata: Beyond the (F,G)-fragment. In: Van Hung, D., Ogawa, M. (eds.) ATVA 2013. LNCS, vol. 8172, pp. 24–39. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  2. 2.
    Baier, C., Katoen, J.P.: Principles of Model Checking. MIT Press (2008)Google Scholar
  3. 3.
    Benedikt, M., Lenhardt, R., Worrell, J.: Two variable vs. linear temporal logic in model checking and games. Logical Methods in Computer Science 9(2) (2013)Google Scholar
  4. 4.
    Boker, U., Kuperberg, D., Kupferman, O., Skrzypczak, M.: Nondeterminism in the presence of a diverse or unknown future. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds.) ICALP 2013, Part II. LNCS, vol. 7966, pp. 89–100. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  5. 5.
    Bustan, D., Rubin, S., Vardi, M.Y.: Verifying ω-regular properties of Markov chains. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 189–201. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  6. 6.
    Clarke, E., Grumberg, O., Peled, D.: Model Checking. MIT Press (2000)Google Scholar
  7. 7.
    Courcoubetis, C., Yannakakis, M.: The complexity of probabilistic verification. Journal of ACM 42(4), 857–907 (1995)CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Couvreur, J.M., Saheb, N., Sutre, G.: An optimal automata approach to LTL model checking of probabilistic systems. In: Vardi, M.Y., Voronkov, A. (eds.) LPAR 2003. LNCS, vol. 2850, pp. 361–375. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  9. 9.
    Dwyer, M., Avrunin, G., Corbett, J.: Patterns in property specifications for finite-state verification. In: ICSE 1999, pp. 411–420. ACM (1999)Google Scholar
  10. 10.
    Etessami, K., Holzmann, G.J.: Optimizing Büchi automata. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 153–167. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  11. 11.
    Gastin, P., Oddoux, D.: Fast LTL to Büchi automata translation. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 53–65. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  12. 12.
    Grädel, E., Thomas, W., Wilke, T. (eds.): Automata, Logics, and Infinite Games. LNCS, vol. 2500. Springer, Heidelberg (2002)MATHGoogle Scholar
  13. 13.
    Henzinger, T., Piterman, N.: Solving games without determinization. In: Ésik, Z. (ed.) CSL 2006. LNCS, vol. 4207, pp. 395–410. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  14. 14.
    Klein, J., Baier, C.: Experiments with deterministic ω-automata for formulas of linear temporal logic. Theoretical Computer Science 363(2), 182–195 (2006)CrossRefMATHMathSciNetGoogle Scholar
  15. 15.
    Klein, J., Baier, C.: On-the-fly stuttering in the construction of deterministic ω-automata. In: Holub, J., Žďárek, J. (eds.) CIAA 2007. LNCS, vol. 4783, pp. 51–61. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  16. 16.
    Klein, J., Müller, D., Baier, C., Klüppelholz, S.: Are good-for-games automata good for probabilistic model checking (extended version). Tech. rep., Technische Universität Dresden (2013), http://wwwtcs.inf.tu-dresden.de/ALGI/PUB/LATA14/
  17. 17.
    Křetínský, J., Garza, R.L.: Rabinizer 2: Small deterministic automata for LTL ∖  GU. In: Van Hung, D., Ogawa, M. (eds.) ATVA 2013. LNCS, vol. 8172, pp. 446–450. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  18. 18.
    Kupferman, O., Piterman, N., Vardi, M.: Safraless compositional synthesis. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 31–44. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  19. 19.
    Kupferman, O., Rosenberg, A.: The blow-up in translating LTL to deterministic automata. In: van der Meyden, R., Smaus, J.-G. (eds.) MoChArt 2010. LNCS, vol. 6572, pp. 85–94. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  20. 20.
    Kupferman, O., Vardi, M.: From linear time to branching time. ACM Transactions on Computational Logic 6(2), 273–294 (2005)CrossRefMathSciNetGoogle Scholar
  21. 21.
    Kupferman, O., Vardi, M.: Safraless decision procedures. In: FOCS 2005, pp. 531–542. IEEE Computer Society (2005)Google Scholar
  22. 22.
    Kwiatkowska, M., Norman, G., Parker, D.: Probabilistic symbolic model checking with PRISM: A hybrid approach. International Journal on Software Tools for Technology Transfer (STTT) 6(2), 128–142 (2004)Google Scholar
  23. 23.
    Kwiatkowska, M., Norman, G., Sproston, J.: Probabilistic model checking of the IEEE 802.11 wireless local area network protocol. In: Hermanns, H., Segala, R. (eds.) PROBMIV 2002, PAPM-PROBMIV 2002, and PAPM 2002. LNCS, vol. 2399, pp. 169–187. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  24. 24.
    Latvala, T.: Efficient model checking of safety properties. In: Ball, T., Rajamani, S.K. (eds.) SPIN 2003. LNCS, vol. 2648, pp. 74–88. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  25. 25.
    Löding, C.: Optimal bounds for transformations of ω-automata. In: Pandu Rangan, C., Raman, V., Sarukkai, S. (eds.) FST TCS 1999. LNCS, vol. 1738, pp. 97–109. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  26. 26.
    Michel, M.: Complementation is more difficult with automata on infinite words. CNET, Paris (1988)Google Scholar
  27. 27.
    Morgenstern, A., Schneider, K.: From LTL to symbolically represented deterministic automata. In: Logozzo, F., Peled, D.A., Zuck, L.D. (eds.) VMCAI 2008. LNCS, vol. 4905, pp. 279–293. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  28. 28.
    Piterman, N.: From nondeterministic Büchi and Streett automata to deterministic parity automata. Logical Methods in Computer Science 3(3:5), 1–21 (2007)Google Scholar
  29. 29.
    Piterman, N., Pnueli, A.: Faster solutions of Rabin and Streett games. In: LICS 2006, pp. 275–284. IEEE (2006)Google Scholar
  30. 30.
    Puterman, M.: Markov Decision Processes: Discrete Stochastic Dynamic Programming. John Wiley & Sons, Inc., New York (1994)CrossRefMATHGoogle Scholar
  31. 31.
    Safra, S.: On the complexity of ω-automata. In: FOCS, pp. 319–327. IEEE (1988)Google Scholar
  32. 32.
    Schewe, S.: Tighter bounds for the determinisation of Büchi automata. In: de Alfaro, L. (ed.) FOSSACS 2009. LNCS, vol. 5504, pp. 167–181. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  33. 33.
    Somenzi, F., Bloem, R.: Efficient Büchi automata from LTL formulae. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 248–263. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  34. 34.
    Vardi, M., Wolper, P.: An automata-theoretic approach to automatic program verification. In: LICS 1986, pp. 332–344. IEEE Computer Society (1986)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Joachim Klein
    • 1
  • David Müller
    • 1
  • Christel Baier
    • 1
  • Sascha Klüppelholz
    • 1
  1. 1.Institute of Theoretical Computer ScienceTechnische Universität DresdenDresdenGermany

Personalised recommendations